Recombination and Fragmentation of Hadrons from a Dense Parton Phase

1. Recombination and Fragmentation of Hadrons from a Dense Parton Phase Rainer J. Fries University of Minnesota Talk at the RIKEN Workshop on Flow and Collective Phenomena BNL, November 19, 2003 • R.J. Fries, C. Nonaka, B. Müller & S.A. Bass, PRL 90, 202303 (2003) • R.J. Fries, C. Nonaka, B. Müller & S.A. Bass, nucl-th/0305079, JPG t.a. • R.J. Fries, C. Nonaka, B. Müller & S.A. Bass, PRC 68, 044902 (2003) • C. Nonaka, R.J. Fries & S.A. Bass, nucl-th/0308051, submitted to PLB Rainer J. Fries

2. Outline • Motivation: hadron spectra, ratios and flow at RHIC • The recombination idea • Calculations using recombination + fragmentation • v2 scaling Rainer J. Fries

3. Jet quenching: suppression of hard particle production Central Au+Aucollisions: suppression of pions by a factor ~5 Suppression of hard (pQCD) hadron production Rainer J. Fries

4. Baryon enhancement at high pt • For pt>2 GeV, protons are as abundant as pions and kaons! • hadron production via fragmentation yields p/π ratio of ~0.1 • where does the large proton over pion ratio at high pt come from? • Why do mesons differ from hadrons? Rainer J. Fries

5. Elliptic flow of K0 and  • hyperon v2 saturates later and higher than kaon v2. • same effect observed for protons and pions. • what drives the different pT scales for KS and Λ v2? • novel mechanism of baryon formation? Sorensen SQM 2003 Rainer J. Fries

6. A possible solution to the puzzle: • parton recombination Where is pQCD? Rainer J. Fries

7. Recombination vs Fragmentation Fragmentation: • for exponential parton spectrum, recombination is more effective than fragmentation • baryons are shifted to higher pt than mesons, for same quark distribution • understand behavior of protons! fragmenting parton: ph = z p, z<1 recombining partons: p1+p2=ph Rainer J. Fries

8. The recombination idea basic assumptions: • at low pt, quarks and antiquarks recombine into hadrons on a hadronization hypersurface: • hadron momentum P is much larger than masses and momentum scales of the wave function of the hadron; • features of the parton spectrum are shifted to higher pt in the hadron spectrum • parton spectrum has thermal part (effective quarks) and a power law tail (quarks and gluons) from pQCD. Rainer J. Fries

9. The nine lives of recombination High Energy Physics Phenomenology: • K.P. Das & R.C. Hwa, Phys. Lett. B68, 459 (1977) Quark-Antiquark Recombination in the Fragmentation Region • description of leading particle effect (field of recent activity!) Heavy-Ion Phenomenology: • T. S. Biro, P. Levai & J. Zimanyi, Phys. Lett. B347, 6 (1995) ALCOR: a dynamical model for hadronization • yields and ratios via counting of constituent quarks • R.C. Hwa & C.B. Yang, PRC66, 025205 (2002) • R. Fries, B. Mueller, C. Nonaka & S.A. Bass, Phys. Rev. Lett. 90 • V. Greco, C.M. Ko and P. Levai, Phys. Rev. Lett. 90 Anisotropic flow: • S. Voloshin, QM2002, nucl-ex/020014 • Z.W. Lin & C.M. Ko, Phys. Rev. Lett 89, 202302 (2002) • D. Molnar & S. Voloshin, nucl-th/0302014 Rainer J. Fries

10. Recombination formalism I Express number of mesons by the quark density matrix . Introduce 2-quark and meson Wigner functions W, . Rainer J. Fries

11. Recombination formalism II choose a hypersurface Σ for hadronization use local light cone coordinates (hadron defining the + axis) wa(r,p):single particle distribution functions for quarks at hadronization ФM & ФB:light-cone wave-functions for the meson & baryon respectively x, x’ & (1-x): momentum fractions carried by the quarks integrating out transverse degrees of freedom yields: Rainer J. Fries

12. important features: ph = Σ pq d3N/dp3h (wq)n (with n=2,3) • for an exponential distribution: Recombination of an exponential spectrum • product of all distribution functions only depends on hadron momentum! • results are insensitive to the model used for recombination • Baryon/Meson ratio is independent of momentum, e.g. (Cp, Cπ : degeneracy factors) Rainer J. Fries

13. Recombination vs. Fragmentation Fragmentation… …nevercompetes with recombination for a thermal (exponential) spectrum: … but it wins out at large pT, when the spectrum is a power law ~ (pT)-b : Rainer J. Fries

14. Recombination + Fragmentation • Fragmentation of perturbative partons dominates at high pt. • Recombination kicks in at 4-6 GeV at RHIC energies. • Our description of recombination fails when /PT and m/PT corrections become large (from 1-2 GeV on at RHIC). • But: recombination will still be the dominant hadronization mechanism. Take into account binding energies, mass effects. Rainer J. Fries

15. Results & Comparison to Data • hadron spectra • hadron ratios • RAA Rainer J. Fries

16. Input and Parameters I Input for the model is the momentum distributions of constituent quarks and anti-quarks at the time of hadronization • the quark distribution is assumed to have a low pt thermalcomponent and a high pt pQCD mini-jet component • the thermal component is parameterized as: with a flavor dependent fugacity ga, temperature T, rapidity width Δ and transverse distribution f(ρ,ф). • the pQCD component is parameterized as: with parameters C, B and β taken from a lo pQCD calculation Rainer J. Fries

17. Input and parameters II Use hypersurface  with t2-z2=2;  = 5 fm/c. Fix T=175 MeV Determine: • Radial flow =0.55 c • Emission volume • Energy loss parameter • Fugacities Rainer J. Fries

18. Hadron Spectra I Rainer J. Fries

19. Hadron Spectra II Rainer J. Fries

20. Hadron Ratios vs. pt Rainer J. Fries

21. Elliptic Flow anisotropic or “elliptic” flow is sensitive to initial geometry low pt domain: high pt domain: more flow in collision plane than perpendicular to it less absorption in collision plane than perpendicular to it total elliptic flow is the sum of both contributions: r(pt): relative weight of the recombination contribution in spectra Rainer J. Fries

22. Elliptic Flow: partons at low pt azimuthal anisotropy of parton spectra is determined by elliptic flow: (Фp: azimuthal angle in p-space) with Blastwave parametrization for parton spectra: azimuthal anisotropy is parameterized in coordinate space and is damped as a function of pt: Rainer J. Fries

23. Parton Number Scaling of Elliptic Flow in the recombination regime, meson and baryon v2 can be obtained from the parton v2 in the following way: • neglecting quadratic and cubic terms, one finds a simple scaling law: Rainer J. Fries

24. Results & Comparison to Data • elliptic flow Rainer J. Fries

25. Elliptic Flow: Input parton elliptic flow: relative weight of recombination: grey area: region of uncertainty for limiting behavior of R & F hadron v2 calcuated separately for R and F and superimposed via: Rainer J. Fries

26. Flavor Dependence of Recombination • Recombination describes measured flavor-dependence! Rainer J. Fries

27. Elliptic Flow: Recombination vs. Fragmentation • high pt: v2 for all hadrons merge, since v2 from energy-loss is flavor blind • charged hadron v2 for high pt shows universal & limiting fragmentation v2 • quark number scaling breaks down in the fragmentation domain Rainer J. Fries

28. Bill Zajc (DNP Tucson) • smoking gun for recombination • measurement of partonic v2 ! • New PHENIX Run-2 result on v2 of 0’s: • New STAR Run-2 result on v2 for ’s: • ALL hadrons measured to date obey quark recombination systematics PHENIX Preliminary p0 X STAR Preliminary Rainer J. Fries

29. New developments I • Another test: the  meson. Do we see a mass effect or the valence quark structure of hadrons? • Reco differs from hydro! • The deuteron and the pentaquark should have tremendous v2. • STAR: deuteron v2 follows the scaling law! Rainer J. Fries

30. New developments II The + will be measured at RHIC. Will v2 scale with n=5? What about other resonances? Influence of the hadronic stage? Rainer J. Fries

31. Summary & Outlook The Recombination + Fragmentation Model: • provides a natural solution to the baryon puzzle at RHIC • describes the intermediate and high pt range of • hadron ratios & spectra • jet-quenching phenomena • elliptic flow • provides a microscopic basis for the Statistical Model • One universal parametrization of the parton phase can explain the data! • v2: proof of collectivity in the parton phase issues to be addressed in the future: • entropy & energy • resonances and influence of the hadronic phase • need improved data of identified hadrons at high pt Rainer J. Fries

32. The End Rainer J. Fries

33. Centrality Dependence of Spectra & Ratios R+F model applicable over full range of centrality deviations from SM as soon as fragmentation sets in low pt deviations due to neglected const. quark mass Rainer J. Fries

34. Flavor Dependence of high-pt Suppression R+F model describes different RAA behavior of protons and pions Lambda’s already exhibit drop into the fragmentation region in the fragmentation region all hadron flavors exhibit jet-quenching Rainer J. Fries

35. Elliptic Flow: partons at high pt azimuthal anisotropy is driven by parton energy/momentum loss Δpt L: average thickness of the medium the unquenched parton pt distribution is shifted by Δpt. • v2 is then calculated via: Rainer J. Fries

36. double parton scattering scales: meson A A pQCD approach to parton recombination single parton scattering and fragmentation scales: T. Ochiai, Prog. Theor. Phys. 75 (1986) 1184 Rainer J. Fries

37. New developments III Can we distinguish production scenarios for the pentaquark? 5q recombination K+N recombination & coalescence, K+N fragmentation & coalescence K+N fragmentation & coalescene in a jet cone (= 5q fragmentation) Even obtain information about the structure? Rainer J. Fries